Many tool handles, such as hammer handles, are constructed of a metal, a synthetic or a composite material. Steel and fiberglass, for example, are often used for tool handle construction. These materials offer reduced materials cost, uniformity of structure and the ability to securely and permanently affix the hammer head or other tool head to the handle. Metal, synthetic and composite handles are relatively durable as compared to wooden handles. Metal, synthetic and composite handles have some disadvantages, however. These handles tend to transfer torque (twisting about the longitudinal axis of the handle) and kinetic energy to a user's hand when a workpiece is impacted. Many hammers with metal or synthetic handles are provided with rubber or rubber-like sleeves at the free end opposite the hammer head to provide a degree of impact protection for the hand of the user. Most of these sleeves are constructed of a relatively hard, non-cushioned single material, however, and provide little or no damping. In addition, such sleeves are not engineered to address torque or torsional force applied to the user's hand that may result when the hammer head “offstrikes,” for example, when the head face misses the intended target, and the side of the head hits a structure such that the impact tends to twist the hammer about a longitudinal axis of the hammer handle. U.S. Pat. No. 6,370,986 (of same Assignee as the present invention), hereby incorporated by reference in its entirety, discloses a hammer with a cushioning grip. It has been found, however, that the teachings of this patent do not sufficiently address torsional or twisting forces imparted to the hammer during impact. A need exists for an impact tool grip that can be used on metal, composite and synthetic handles that provides a high degree of torque absorption and cushioning to reduce the kinetic energy transferred to the user's hand during impact and that can be applied to these handles easily during the manufacturing process.